Image zero watermarking method based on fractional order generalized pseudo Jacobi-Fourier moment

Abstract

The invention discloses an image zero watermarking method based on a fractional order generalized pseudo Jacobi-Fourier moment, which comprises the following steps: firstly, extracting three color components of a host image, re-dividing and interpolating the color components by using a polar coordinate pixel tiling method, and calculating a moment value of the fractional order generalized pseudo Jacobi-Fourier moment FGPJFMs; secondly, considering different influences of different generalized parameters and fractional order parameters on extracted image feature information, selecting a group of different generalized parameters and fractional order parameters to construct a mixed low-moment feature, and quantizing a feature vector; secondly, converting the quantized feature vector into a feature map by using an asymmetric Tent mapping method, scrambling the watermark and the feature map by using transformation, and performing XOR operation on the watermark and the feature map to obtain a target zero watermark; and finally, the zero watermark, the secret key and the identification information of the copyright owner are sent to the trusted authority in a confidential mode, and the authority affixes a timestamp.

Description

Technical Field

[0001] The invention belongs to the technical field of color image copyright protection, and relates to an image zero watermark method based on fractional-order generalized pseudo-Jacobi-Fourier moment. Background Art

[0002] Traditional digital watermarking technology embeds copyright information and hides it by changing the original digital image. This method will inevitably damage the digital image and is not allowed in fields such as medicine and military that have extremely strict requirements on image details. In addition, the extracted watermark image may be distorted.

[0003] The zero watermark method does not change the information of the host image. It only needs to extract the important features of the image to construct the zero watermark image. In the experiment, it showed good concealment, overcoming the contradictions of traditional watermark algorithms in watermark capacity, concealment, and robustness, achieving a good balance, and promoting the development of copyright protection technology. However, there are still potential factors that affect the comprehensive evaluation performance of five aspects: robustness, distinguishability, security, speed, and capacity.

[0004] The existing zero-watermark methods are generally divided into three types: spatial domain features, frequency domain features, and moment features. Among them, the zero-watermark method based on moment features uses moments and moment invariants to construct watermark information. Compared with other extraction methods, image moments are invariant and can still detect the correct watermark after being attacked by various attacks, which has good robustness. However, the zero-watermark method based on moments has the following problems: First, the pursuit of robustness is single, and the distinction is not given enough attention in experiments and analysis, resulting in a high false detection rate; second, most of them are oriented to grayscale images, and there are few algorithms applicable to color images. Some methods applicable to color images only calculate a single color channel component; third, the direct calculation of moment values ​​has high time complexity, numerical instability, and poor precision. Summary of the invention

[0005] In view of the above technical problems existing in the prior art zero-watermarking method based on moment features, the present invention proposes an image zero-watermarking method based on fractional-order generalized pseudo-Jacobi-Fourier moments.

[0006] The technical solution of the present invention is: an image zero watermarking method based on fractional-order generalized pseudo-Jacobi-Fourier moment, which is performed according to the following steps:

[0007] a. Initial Setup

[0008] Get the host image I and initialize the variables α = {5, 10, 15, 20, 50}, h = {0.25, 0.5, 1, 2, 4}, where α and h represent the generalized parameters and fractional order parameters of the basis function of the fractional generalized pseudo-Jacobi-Fourier moment, respectively; set the fractional generalized pseudo-Jacobi-Fourier moment coefficient Hnmαh The maximum order is k, where n represents the current order and m represents the number of repetitions; Initialize the watermark image for copyright authentication: W = {w(x,y):w∈{0,1},(x,y)∈[1,N W ] 2},N W Refers to the watermark image size; Initialization key: key1 = {x 0 =0.5,μ=0.45,n=N W}, key2 = {a = 2, b = 3, It = 10}, key3 = {a = 1, b = 2, It = 5}; Set the pixel block Ω after redivision in the polar coordinate system u,v The starting radius is The final radius is The starting angle is The final angle is The final center point radius of the pixel block is The center angle is Where ρ represents the radius, θ represents the angle, u represents the number of rings in which the pixel block is located, and v represents the number of rings in which the pixel block is located. Set the node position of the Gaussian integral to Z k , the weight of this node is η k ;

[0009] b. Use fractional generalized pseudo-Jacobi-Fourier moments FGPJFMs to obtain zero watermark:

[0010] b.1 Get the red, green, and blue color channel components f of the host image I R [i,j],f G [i,j] and f B [i,j] are re-divided according to the polar coordinate pixel tiling algorithm, and the pixels obtained by division are marked as Ω u,v ,f(ρ uv ,θ u,v ) is f(r i,j ,θ i,j ) in pixel block Ω u,v The nearest interpolation of the divided color channel component f R [ρ uv, θ uv ]、f G [ρ uv, θ uv ] and f B [ρ uv, θ uv ];

[0011] b.2 The calculated f R [ρ uv, θ uv ]、fG [ρ uv, θ uv ] and f B [ρ uv, θ uv The coefficients H of the fractional generalized pseudo-Jacobi-Fourier moments FGPJFMs of nmαh (f R ), H nmαh (f G ) and H nmαh (f B ), the calculation process is:

[0012]

[0013] in:

[0014]

[0015] P n (α,h,ρ)=(L 1 ρ h +L 2 ) n-1 (α,h,ρ)+L 3 P n-2 (α,h,ρ),n≥2,

[0016]

[0017] b.3 Based on the fractional generalized pseudo-Jacobi-Fourier moment FGPJFMs coefficient H nmαh (f R ), H nmαh (f G ) and H nmαh (f B ), and the quaternion fractional-order generalized pseudo-Jacobi-Fourier moment coefficient matrix is ​​calculated

[0018] b.4 Generate mixed low-order moment features v:

[0019] Among them, n is the order, m is the number of repetitions, and k is the maximum order. is the fractional-order generalized pseudo-Jacobi-Fourier moment coefficient of the quaternion;

[0020] b.5 Quantize the mixed low-order moment eigenvector v to obtain the quantized eigenvector Where median(@) means taking the median value, mean(·) means taking the mean value;

[0021] b.6 Using asymmetric Tent mapping to obtain the chaotic sequence {x t}:

[0022] Among them, μ is the control parameter, t is the number of iterations;

[0023] b.7 According to the calculated quantized eigenvector bv and chaotic sequence {x t}Perform left, right and circular shift operations to generate feature map B;

[0024] b.8 Use key key3 to scramble the feature map B, and use key key2 to scramble the watermark image W; the scrambling method used is the generalized Arnold transform, and the specific formula is: Among them, p and q are scrambling parameters;

[0025] b.9 Perform an XOR operation on the scrambled watermark image WS and the scrambled feature map BS to generate a zero watermark image ZW; ZW = XOR (WS, BS);

[0026] b.10 Send the zero watermark ZW, key and copyright owner’s identification information to a trusted authority in a confidential manner, and the authority will stamp the zero watermark ZW with a timestamp;

[0027] c. Use fractional generalized pseudo-Jacobi-Fourier moments FGPJFMs to verify zero watermark:

[0028] c.1 Before verification, the user obtains the zero watermark, key, copyright owner's identification information and timestamp from the authority and verifies them;

[0029] c.2. Execute steps b.1 to b.7 of the zero watermark acquisition stage on the image to be detected I′ to generate a feature map B′ of the image to be detected;

[0030] c.3 The feature map B' of the image to be detected is scrambled by generalized Arnold transform to obtain the feature map BS';

[0031] c.4 Perform an XOR operation on the scrambled feature map BS' and the zero-watermark image ZW downloaded and verified from the authority to obtain WS'; WS' = XOR (BS', ZW);

[0032] c.5 Descramble WS' to obtain the detected watermark.

[0033] The invention provides an image zero watermark method based on fractional-order generalized pseudo-Jacobi-Fourier moments. First, three color components of a host image are extracted, and the color components are re-divided and interpolated by using a polar coordinate pixel tiling method, and the moment values ​​of the fractional-order generalized pseudo-Jacobi-Fourier moments FGPJFMs are calculated; secondly, considering the different effects of different generalized parameters and fractional-order parameters on the extracted image feature information, a set of different generalized parameters and fractional-order parameters are selected to construct a mixed low-order moment feature, and the feature vector is quantized; then, the quantized feature vector is converted into a feature map by using an asymmetric Tent mapping method, and the watermark and the feature map are scrambled by using a transformation, and an exclusive-OR (XOR) operation is performed on them to obtain a target zero watermark; finally, the zero watermark, the key, and the identification information of the copyright owner are sent to a trusted authority in a confidential manner, and the authority stamps the zero watermark, the key, and the identification information of the copyright owner. Experimental results show that the method provided by the present invention has a very good defense effect against various attacks because it simultaneously selects generalized parameters and fractional-order parameters to construct mixed low-order moment features, can well balance distinguishability and robustness, and performs well in terms of security, watermark capacity, and calculation speed.

[0034] Compared with the existing technology, the solution of the present invention has the following improved characteristics:

[0035] First, a hybrid low-order moment feature based on the fractional generalized pseudo-Jacobi-Fourier moment FGPJFMs is used to describe the image. The zero point distribution of the fractional generalized pseudo-Jacobi-Fourier is controlled by the generalization parameter and the fractional order parameter at the same time. When the fractional order parameter is greater than 1, the ability to describe the external features is strong. When the fractional order parameter is less than 1, the ability to describe the central area features is strong. The larger the generalization parameter, the closer the basis function zero point is to 0. In order to improve the robustness to various attacks and balance the distinguishability, the present invention selects a group of parameters α = {5, 10, 15, 20, 50}, h = {0.25, 0.5, 1, 2, 4} to construct features. Users can choose different parameter combinations to meet the requirements for feature extraction according to different task objects and application situations.

[0036] Second, a new fractional-order generalized pseudo-Jacobi-Fourier moment FGPJFMs calculation scheme is proposed. The present invention adopts recursive calculation and polar coordinate pixel tiling algorithm for the traditional generalized pseudo-Jacobi-Fourier moment GPJFMs, and expands the fractional order and quaternion. Compared with the traditional generalized pseudo-Jacobi-Fourier moment GPJFMs, this method has the advantages of low time complexity, high precision, numerical stability, and strong feature description ability, thereby improving the performance of the zero-watermark method in all aspects and broadening the scope of application.

[0037] Third, based on the traditional moment, the quaternion calculation method is introduced to expand the application scope of the moment from grayscale images to the copyright protection of color images. Compared with the traditional single color channel calculation and the method of converting color images into grayscale images, the present invention takes into account the correlation between color channels and information, and has a better effect on the copyright protection of color images. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] FIG. 1 is a diagram showing the watermark detection and bit error rate results of a color image Lena after being attacked according to an embodiment of the present invention.

[0039] FIG. 2 is a diagram showing the discrimination comparison results of an embodiment of the present invention and other algorithms in the Coil-100 color image library.

[0040] Figure 3 This is a graph showing the relationship between the watermark capacity and the generalized parameter, the number and order of fractional-order parameters according to an embodiment of the present invention.

[0041] Figure 4 This is a diagram showing the speed calculation results according to an embodiment of the present invention.

[0042] Figure 5 This is a diagram showing the key change and verification accuracy results in an embodiment of the present invention.

[0043] Figure 6 This is a flow chart of obtaining a zero watermark according to an embodiment of the present invention.

[0044] Figure 7 This is a flow chart of verifying zero watermark according to an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The present invention provides an image zero watermarking method based on fractional-order generalized pseudo-Jacobi-Fourier moment, and the specific operation process is as follows: Figure 6 , Figure 7 As shown, follow the steps below:

[0046] a. Initial Setup

[0047] Get the host image I and initialize the variables α = {5, 10, 15, 20, 50}, h = {0.25, 0.5, 1, 2, 4}, where α and h represent the generalized parameters and fractional order parameters of the basis function of the fractional generalized pseudo-Jacobi-Fourier moment, respectively; set the fractional generalized pseudo-Jacobi-Fourier moment coefficient H nmαh The maximum order is k, where n represents the current order and m represents the number of repetitions; Initialize the watermark image for copyright authentication: W = {w(x,y):w∈{0,1},(x,y)∈[1,N W ] 2},N W Refers to the watermark image size; Initialization key: key1 = {x0 =0.5,μ=0.45,n=N W}, key2 = {a = 2, b = 3, It = 10}, key3 = {a = 1, b = 2, It = 5}; Set the pixel block Ω after redivision in the polar coordinate system u,v The starting radius is The final radius is The starting angle is The final angle is The final center point radius of the pixel block is The center angle is Where ρ represents the radius, θ represents the angle, u represents the number of rings in which the pixel block is located, and v represents the number of rings in which the pixel block is located. Set the node position of the Gaussian integral to Z k , the weight of this node is η k ;

[0048] b. Use fractional generalized pseudo-Jacobi-Fourier moments FGPJFMs to obtain zero watermark:

[0049] b.1 Get the red, green, and blue color channel components f of the host image I R [i,j],f G [i,j] and f B [i,j] are re-divided according to the polar coordinate pixel tiling algorithm, and the pixels obtained by division are marked as Ω u,v ,f(ρ uv ,θ u,v ) is f(r i,j ,θ i,j ) in pixel block Ω u,v The nearest interpolation of the divided color channel component f R [ρ uv, θ uv ]、f G [ρ uv, θ uv ] and f B [ρ uv, θ uv ];

[0050] b.2 The calculated f R [ρ uv, θ uv ]、f G [ρ uv, θ uv ] and f B [ρ uv, θ uv The coefficients H of the fractional generalized pseudo-Jacobi-Fourier moments FGPJFMs of nmαh (f R ), Hnmαh (f G ) and H nmαh (f B ), the calculation process is:

[0051]

[0052] in:

[0053]

[0054]

[0055] P n (α,h,ρ)=(L 1 ρ h +L 2 ) n-1 (α,h,ρ)+L 3 P n-2 (α,h,ρ),n≥2,

[0056]

[0057] b.3 Based on the fractional generalized pseudo-Jacobi-Fourier moment FGPJFMs coefficient H nmαh (f R ), H nmαh (f G ) and H nmαh (f B ), and the quaternion fractional-order generalized pseudo-Jacobi-Fourier moment coefficient matrix is ​​calculated

[0058] b.4 Generate mixed low-order moment features v:

[0059] Among them, n is the order, m is the number of repetitions, and k is the maximum order. is the fractional-order generalized pseudo-Jacobi-Fourier moment coefficient of the quaternion;

[0060] b.5 Quantize the mixed low-order moment eigenvector v to obtain the quantized eigenvector Where median(·) means taking the median value, and mean(·) means taking the mean value;

[0061] b.6 Using highly secure asymmetric Tent mapping to obtain the chaotic sequence {x t}:

[0062] Among them, μ is the control parameter, t is the number of iterations;

[0063] b.7 According to the calculated quantized eigenvector bv and chaotic sequence {x t}Perform left, right and circular shift operations to generate feature map B;

[0064] b.8 Use key key3 to scramble the feature map B, and use key key2 to scramble the watermark image W; the scrambling method used is the generalized Arnold transform, and the specific formula is: Among them, p and q are scrambling parameters;

[0065] b.9 Perform an XOR operation on the scrambled watermark image WS and the scrambled feature map BS to generate a zero watermark image ZW: ZW = XOR (WS, BS);

[0066] b.10 Send the zero watermark ZW, key and copyright owner’s identification information to a trusted authority in a confidential manner, and the authority will stamp the zero watermark ZW with a timestamp;

[0067] c. Use fractional generalized pseudo-Jacobi-Fourier moments FGPJFMs to verify zero watermark:

[0068] c.1 Before verification, the user must obtain the zero watermark, key, copyright owner's identification information and timestamp from the authority and verify them;

[0069] c.2. Execute steps b.1 to b.7 of the zero watermark acquisition stage on the image to be detected I′ to generate a feature map B′ of the image to be detected;

[0070] c.3 Scramble B' by generalized Arnold transformation to obtain BS';

[0071] c.4 Perform an XOR operation on the scrambled feature map BS' and the zero-watermark image ZW downloaded and verified from the authority to obtain WS': WS' = XOR (BS', ZW);

[0072] c.5 Descramble WS' to obtain the detected watermark.

[0073] Experimental test and parameter setting:

[0074] The experimental environment of this experiment is Matlab R2018a. The test images used in the experiment are the color image Lena and the image library Coil-100, both of which are publicly available on the Internet.

[0075] In FIG. 1 , ab are diagrams showing the watermark detection and bit error rate results after the color image Lena is attacked according to an embodiment of the present invention.

[0076] FIG2 is a diagram showing the distinguishing comparison results of an embodiment of the present invention and other algorithms in the Coil-100 color image library, wherein (a) is the comparison algorithm and (b) is the algorithm proposed by the present invention.

[0077] Figure 3 This is a graph showing the relationship between the watermark capacity and the generalized parameter, the number and order of fractional-order parameters according to an embodiment of the present invention.

[0078] Figure 4 This is a diagram showing the speed calculation results according to an embodiment of the present invention.

[0079] Figure 5 This is a diagram showing the key change and verification accuracy results in an embodiment of the present invention.

[0080] Figure 6 This is a flow chart of obtaining a zero watermark according to an embodiment of the present invention.

[0081] Figure 7 This is a flow chart of verifying zero watermark according to an embodiment of the present invention.

[0082] References used in Figure 2:

[0083] Wang X, Wang L, Tian J, et al. Color Image Zero-Watermarking Using Accurate Quaternion Generalized Orthogonal Fourier-Mellin Moments[J]. Journal of Mathematical Imaging and Vision, 2021, 63(6): 1-27.

Claims

1. An image zero watermarking method based on fractional generalized pseudo-Jacobi-Fourier moment, characterized in that Follow these steps: a. Initial Setup Get the host image I and initialize the variables α = {5, 10, 15, 20, 50}, h = {0.25, 0.5, 1, 2, 4}, where α and h represent the generalized parameters and fractional order parameters of the basis function of the fractional generalized pseudo-Jacobi-Fourier moment, respectively; set the fractional generalized pseudo-Jacobi-Fourier moment coefficient H nmαh The maximum order is k, where n represents the current order and m represents the number of repetitions; Initialize the watermark image for copyright authentication: W = {w(x,y):w∈{0,1},(x,y)∈[1,N W ] 2 },N W Refers to the watermark image size; Initialization key: key1 = {x0 = 0.5, μ = 0.45, n = N W }, key2 = {a = 2, b = 3, It = 10}, key3 = {a = 1, b = 2, It = 5}; Set the pixel block Ω after redivision in the polar coordinate system u,v The starting radius is The final radius is The starting angle is The final angle is The final center point radius of the pixel block is The center angle is Where ρ represents the radius, θ represents the angle, u represents the number of rings in which the pixel block is located, and v represents the number of rings in which the pixel block is located. Set the node position of the Gaussian integral to Z k , the weight of this node is η k ; b. Use fractional generalized pseudo-Jacobi-Fourier moments FGPJFMs to obtain zero watermark: b.1 Get the red, green, and blue color channel components f of the host image I R [i,j],f G [i,j] and f B [i,j] are re-divided according to the polar coordinate pixel tiling algorithm, and the pixels obtained by division are marked as Ω u,v ,f(ρ uv ,θ u,v ) is f(r i,j ,θ i,j ) in pixel block Ω u,v The nearest interpolation of the divided color channel component f R [ρ uv, θ uv ]、f G [ρ uv, θ uv ] and f B [ρ uv, θ uv ]; b.2 The calculated f R [ρ uv, θ uv ]、f G [ρ uv, θ uv ] and f B [ρ uv, θ uv The coefficients H of the fractional generalized pseudo-Jacobi-Fourier moments FGPJFMs of nmαh (f R ), H nmαh (f G ) and H nmαh (f B ), the calculation process is: in: P n (a,h,ρ)=(L1ρ h +L2)P n-1 (a,h,p)+L3P n-2 (a,h,p),n≥2, b.3 Based on the fractional generalized pseudo-Jacobi-Fourier moment FGPJFMs coefficient H nmαh (f R ), H nmαh (f G ) and H nmαh (f B ), and the quaternion fractional-order generalized pseudo-Jacobi-Fourier moment coefficient matrix is ​​calculated b.4 Generate mixed low-order moment features v: Among them, n is the order, m is the number of repetitions, and k is the maximum order. is the coefficient of the quaternion fractional generalized pseudo-Jacobi-Fourier moment; b.5 Quantize the mixed low-order moment eigenvector v to obtain the quantized eigenvector Where median(@) means taking the median value, mean(@) means taking the mean value; b.6 Using asymmetric Tent mapping to obtain the chaotic sequence {x t }: Among them, μ is the control parameter, t is the number of iterations; b.7 According to the calculated quantized eigenvector bv and chaotic sequence {x t }Perform left, right and circular shift operations to generate feature map B; b.8 Use key key3 to scramble the feature map B, and use key key2 to scramble the watermark image W; the scrambling method used is the generalized Arnold transform, and the specific formula is: Among them, p and q are scrambling parameters; b.9 Perform an XOR operation on the scrambled watermark image WS and the scrambled feature map BS to generate a zero watermark image ZW; ZW = XOR (WS, BS); b.10 Send the zero watermark ZW, key and copyright owner’s identification information to a trusted authority in a confidential manner, and the authority will stamp the zero watermark ZW with a timestamp; c. Use fractional generalized pseudo-Jacobi-Fourier moments FGPJFMs to verify zero watermark: c.1 Before verification, the user obtains the zero watermark, key, copyright owner's identification information and timestamp from the authority and verifies them; c.

2. Execute steps b.1 to b.7 of the zero watermark acquisition stage on the image to be detected I′ to generate a feature map B′ of the image to be detected; c.3 The feature map B' of the image to be detected is scrambled by generalized Arnold transform to obtain the feature map BS'; c.4 Perform an XOR operation on the scrambled feature map BS' and the zero-watermark image ZW downloaded and verified from the authority to obtain WS'; WS' = XOR (BS', ZW); c.5 Descramble WS' to obtain the detected watermark.

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